数学娱乐(五)——推广Fibonacci数列与幂级数和

Mathematical Recreation(Ⅴ):Generalized Fibonacci's Number and Sum of Power Series

推广Fibonacci数列是指a0,a1不为零的实数,an=an-1+an-2,n≥2.本文探讨推广Fibonacci数的性质以及sum from n=0 to ∞ (ankxn)(k=1,2,3)的级数和.

If real numbers an ≠0,a1≠0 and an = an-1 ＋ an-2 ,n ≥2, { an } is called generalized Fibonacci＇ s number. In this paper, the properties of generalized Fibonaeei＇ s number and sum of power series x∑n=0 α^knx^nk=1,2,3 were discussed.